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This is a question from a Statistics class exam that I still am not sure on how to complete.
The number of accidents in a week follows a discrete random variable X with a probability function x|p(x)
0|0.12
1|0.19
2|0.12
3|0.20
4|0.14
5|0.19
6|0.04
calculate $E(e^ {(3x)})$.
We've been working on moment generating functions in class, but each of those take a formula for a single probability like Bin(n,p) or Bern(p), not a table of data. I really need to know step by step how a problem like this works so I can replicate the process for the final with new data.
1 Answer
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$$ E\big(e^{3X}\big) = e^{3\cdot0}P(X=0)+e^{3\cdot1}P(X=1)+e^{3\cdot2}P(X=2)+e^{3\cdot3}P(X=3)+e^{3\cdot4}P(X=4)+e^{3\cdot5}P(X=5)+e^{3\cdot6}P(X=6). $$
